It looks more like a lake that photo not a river. The way the waves are on it would indicate a body of water such as lake or larger tarn. Personally I think there are plenty of places as nice as that in their own way but not quite like it. There are too many of the wrong trees right near the edge I think. We don't have many sites like this I think. Perhaps there are some like it in the southeast but I don't really know that part of the UK. My best guess would be check out Scotland. I have had a family holiday as a kid at Caldron (bad spelling) campsite in Glen Trool in Dumfries and Galloway that had trees right up to the lochside but they were coniferous trees. I think it is closed now too as that was many years ago now.
Personally for woodland I think Glen Affric is hard to beat in the UK. Not sure about woods near water there though as I've yet to have the pleasure of a trip there.
Anyway, you won't find a spot like it in UK I think but you will find places as nice in their own way. Woods on lakes / lochs / loughs are to be found. Camping is of course legal IF you get the landowner's permission anywhere in the UK. Finding the contact details of the landowner is not always as easy, then you have to persuade them you won't do any harm. Of course that is still better than stealth camping as it is legal but even if you get permission then practising stealth camping is still a good idea I think. BTW in the Lakes you will mostly be tolerated if you camp out of site of farms and dwellings, above the intake wall and leave it the next morning as you found the site. There is a long tradition of wildcamping being accepted in the Lakes such that it is as good as being legal as you'll get south of the border providing we all leave no trace. No nappies, food or drink cans or bottles left behind. And above all no used toilet paper in or near streams or places which heavy rain could wash into the waterways!! That includes popular areas like Angletarn near Patterdale (hint to outward bound group leaders who go there).
